They are doing exactly the same as many other apps (Netflix, Spotify and other Email apps like Spark), even their other app (Basecamp) which has been on the store for 7 years!
The rules can be very subjective and inconsistently applied.
They are doing the same as Spotify and Netflix apps. Payment is done outside the app.
You can also make in-app purchases there, if you choose to. You can't with Hey.
You can't make in-app purchases in Spotify. Netflix got rid of in-app purchases for a while, but then renegotiated a new deal with Apple. You can't buy books in Kindle.